Self-similar solutions and large time asymptotics for the dissipative quasi-geostrophic equation

• Autores: José Antonio Carrillo , Lucas C. F. Ferreira
• Localización: Monatshefte für mathematik, ISSN 0026-9255, Vol. 151, Nº 2, 2007, págs. 111-142
• Idioma: inglés
• DOI: 10.1007/s00605-007-0447-7
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• Resumen

  • We analyze the well-posedness of the initial value problem for the dissipative quasi-geostrophic equations in the subcritical case. Mild solutions are obtained in several spaces with the right homogeneity to allow the existence of self-similar solutions. While the only small self-similar solution in the strong space is the null solution, infinitely many self-similar solutions do exist in weak- spaces and in a recently introduced [7] space of tempered distributions. The asymptotic stability of solutions is obtained in both spaces, and as a consequence, a criterion of self-similarity persistence at large times is obtained.